There is no one way to become a successful fitness model. There is no single path or magic secret. There are however some key things a person can do to greatly improve their chances of "making it" in the fitness biz as a model, and perhaps using that success as a launching pad to greater things, such as movies, TV, etc
First, being a fitness model means you stay in shape all the year round. If you're used to the bodybuilder's practice of having a "cutting season" and a "bulking season" say goodbye to the bulking part. You have to stay lean all year round or you will miss photo opportunities. When the magazine editors call you, they want you NOW! If you're not ready, you lose because someone else always is ready. You can't say, "ok, I'll do it, just let me go on a diet for 12 weeks first."
Once you're in great shape, create your own photo portfolio. Research physique photographers in your area and ask to see samples of their work. Also find out whether you get to keep the negatives. Some photographers give you the negatives and then you can make all the copies you want and use them for anything you want. Other photographers give you only prints and if you want more copies, you have to buy them. This is a common practice and I respect the reasons why the photographers do it, but I'd recommend finding someone who gives you the negatives. They're out there. Find out the deal beforehand to avoid misunderstandings. Also get written permission to have the photos published and you'll make sure the photo gets a credit in the magazines
Above all, be willing to hustle. Being a beginner, The magazines are not coming to you, you have to go to them. It's worth it to offer use of your image for free the first time if necessary, because once you get that first break and you've been in a magazine, it gets easier. The next time you send your stuff to a magazine, you include your previous magazine spread, giving you instant credibility as a published fitness model.